So close and yet so far, wouldn't you like to yell at the person filling in the enlistment roster for leaving blank age and place of birth?
Here is what I found: Ancestry.com has this database in searchable form, titled "U.S. Army, Register of Enlistments, 1798-1914" This is their source they cite: "Original data: Register of Enlistments in the U.S. Army, 1798-1914; (National Archives Microfilm Publication M233, 81 rolls); Records of the Adjutant General’s Office, 1780’s-1917, Record Group 94; National Archives, Washington, D.C."
Looking at original page as scanned you have the correct information on first page of ledger, second page has served in 14th Infantry Company C and Discharged July 28th 1848 -end of service-at New Orleans, LA as a pvt.
It is Haile by the way.
What year and where was your Elijah Hanon born and died?